Circumradius of Scalene Triangle given Longer Side and Larger Angle Calculator

Formula Used:

\[ r_c = \frac{S_{Longer}}{2 \times \sin(\angle_{Larger})} \]

Circumradius of Scalene Triangle:

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1. What is the Circumradius of Scalene Triangle?

The Circumradius of a Scalene Triangle is the radius of the circumcircle that passes through all three vertices of the triangle. It represents the distance from the triangle's circumcenter to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{S_{Longer}}{2 \times \sin(\angle_{Larger})} \]

Where:

\( r_c \) — Circumradius of Scalene Triangle (m)
\( S_{Longer} \) — Longer Side of Scalene Triangle (m)
\( \angle_{Larger} \) — Larger Angle of Scalene Triangle (radians)

Explanation: This formula relates the circumradius to the longest side of the triangle and the angle opposite to it, using the sine function from trigonometry.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry for determining properties of the circumcircle, solving triangle problems, and in various engineering applications where circular properties of triangular shapes are relevant.

4. Using the Calculator

Tips: Enter the length of the longer side in meters and the larger angle in degrees. The angle must be between 0° and 180° (exclusive), and the side length must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle is a triangle with all three sides of different lengths and all three angles of different measures.

Q2: Why use the longer side and larger angle specifically?
A: The formula uses the relationship where the side length is proportional to the sine of its opposite angle, making the longer side and its opposite larger angle the most relevant pair.

Q3: Can this formula be used for other types of triangles?
A: Yes, this formula works for all triangles, but it's particularly useful for scalene triangles where side lengths and angles are all different.

Q4: What are the units of measurement?
A: The side length is in meters, the angle in degrees, and the resulting circumradius will be in meters.

Q5: What if I have the other sides and angles?
A: There are alternative formulas using different combinations of sides and angles, but this specific calculator requires the longer side and its opposite larger angle.